Biology · Introductory biology · Worked example
Spot bias in a mark–recapture estimate
A population truly has 300 animals. Sixty are marked, and a second sample catches 75. Predict the recaptures and the Lincoln–Petersen estimate if every animal is equally catchable, if marked animals are trap-happy and twice as likely to be caught, and if they are trap-shy and half as likely.
Equal catchability
Marked animals are 60 of 300, one fifth, so a catch of 75 should hold about 15 of them. The estimate then recovers the true size.
Trap-happy animals
If each marked animal is twice as catchable, the 60 marked count like 120 against the 240 unmarked, so one third of the catch is marked: 25 animals. The estimate drops to 180.
Trap-shy animals
If each marked animal is half as catchable, the 60 count like 30 against 240, so one ninth of the catch is marked, about 8.3 animals. The estimate rises to 540.
Why bigger samples do not help
These are the expected results. A larger second sample would shrink the chance variation around 180 or 540, but it would not move either estimate toward 300: unequal catchability is a bias, not noise. The cure is in the design, such as catching the second sample by a different method.
Result
With equal catchability R = 15 and the estimate is 300. Trap-happy animals give R = 25 and an estimate of 180; trap-shy animals give R ≈ 8.3 and an estimate of 540.
Your turn
In the same population of 300, marks fall off 12 of the 60 marked animals before the second catch of 75. About how many recaptures should appear, and what is the estimate?
Show the answer and explanation
About 12 recaptures and an estimate of 375: lost marks make the population look larger.
Only 48 animals still carry marks, so the catch holds about 75 × 48/300 = 12 of them. The formula still uses M = 60, so N̂ = 60 × 75/12 = 375.
Keep exploring
The mark–recapture tool opens with 60 marked, 75 caught and 25 recaptured, and reports 180: it cannot tell that the animals were trap-happy.
Return to the concept →Sources and scope
Authored study material. Tool results depend on the stated inputs and model assumptions.
Try in the workspace
Open the example inputs, change a value and keep a useful result on your board.
Open the mark–recapture tool Open worked example on a board Mark–recapture equations in Biology ReferenceYour existing work stays on this device. Examples open as editable copies.